Which data set has a greater spread? why? set a: {38, 12, 23, 48, 55, 16, 18} set b: {44, 13, 24, 12, 56} has a greater spread because .

Set B has a greater spread , because it has a higher IQR

Step-by-step explanation:

One way to measure the spread of a data set is to break it into quarters and measure the interquartile range (IQR).

Set A: {38, 12, 23, 48, 55, 16, 18}

(a) Sort the numbers

(12, 16, 18, 23, 38, 48, 55}

(b) First quartile

The median of 12, 16, and18 is 16.

First quartile = 16

(c) Third quartile

The median of 38, 48, and 55 is 48.

Third quartile = 48

(d) IQR

IQR = 48 - 16  = 32

Set B: {44, 13, 24, 12, 56}

(a) Sort the numbers

(12, 13, 24, 44, 56}

(b) First quartile

The median of 12 and 13 is 12.5.

First quartile = 12.5

(c) Third quartile

The median of 44 and 56  is 50.

Third quartile = 50

(d) IQR

IQR = 50 - 12.5 = 37.5

Set B has the greater spread, because it has the higher IQR.

The Box plot below shows that Set B has the greater spread.